Warm-Up What is the solution to: -3k + -5k - (-16k) = 40

Finished with Test? Independent and Dependent Variables Make sure you have finished the Clue game if you want extra credit and showed all work. Get the worksheet on the front desk. Do the worksheet labeled Independent and Dependent Variables first. Review the worksheet you got yesterday with the vocab words on it. Add to your Brain Dump. We will see who has the most today. Work with a partner to match the variables once everyone has finished the test. Homework: Complete worksheet if not finished in class. Write this in your bull book. Extra Credit Project: Will be due next Friday, you will need to pick one scenario with independent and dependent variable and draw a picture of it. More details to come.

In an Algebraic situation, equation, table, or graph, the variables (usually x and y) can be classified as either __________ or _________. independent dependent

Independent Variable The independent variable is always located on the _________ of a graph. The independent variable is the ________________. It is usually the ________ in a table or equation. The independent variable STANDS ALONE (___________). The independent variable is what happens _______. x-axis Input (domain) “x” Does not depend FIRST

The variable in a function whose value is subject to choice is the independent variable. The independent variable affects the value of the dependent variable.

Dependent Variable The dependent variable is always located on the _________ of a graph. The dependent variable is the ______________. It is usually the _______ in a table or equation. The dependent variable DEPENDS on the ________________. The dependent variable is what happens _______. y-axis Output (Range) “y” independent variable 2nd

The variable in a function whose value is determined by the independent variable.

Let’s Practice! 1.A student’s grade depends on how much she studies. Independent variable:__________ Dependent variable:___________ 2. The height of a plant and the amount you water it. Independent variable: ___________ Dependent variable: _____________ Time studying grade Amount watered height

3. The amount of money you make and the number of hours you work. Independent variable: _____________ Dependent variable:_____________ 4. The number of sodas you buy and the total money spent. Independent variable:______________ Dependent variable:_______________ 5. The number of houses you can paint depends on how much time you have. Independent variable:______________ Dependent variable:_______________ Hours worked Amount of money Number of sodas Total money Amount of time Number of houses

Setting the PowerPoint View Use Normal View for the Interactive Elements To use the interactive elements in this presentation, do not select the Slide Show view. Instead, select Normal view and follow these steps to set the view as large as possible: On the View menu, select Normal. Close the Slides tab on the left. In the upper right corner next to the Help button, click the ^ to minimize the ribbon at the top of the screen. On the View menu, confirm that Ruler is deselected. On the View tab, click Fit to Window. Use Slide Show View to Administer Assessment Items To administer the numbered assessment items in this presentation, use the Slide Show view. (See Slide 7 for an example.)

Table of Contents Graphing Equations Equations and Tables Click on a topic to go to that section. Dependent and Independent Variables Translating to Equations

Return to Table of Contents

An equation is a statement that shows that two mathematical expressions are equal. These are examples of equations: 12 + a = 15x / 5 = 10 y = 3x

1The Dolphins scored 9 more points than the Jets. The Jets scored 34 points. Which equation could be used to find the number of points p that the Jets scored? Ap + 9 = 34 Bp + 34 = 9 Cp - 9 = 34 Dp - 34 = 9

2Frank earns $8.50 per hour for mowing his neighbors' yards. Last weekend Frank earned $51. Which equation can be used to determine the number of hours h Frank worked last weekend? A8.5h = 51 B51h = 8.5 C8.5/h = 51 Dh/51 = 8.5

3Melinda and her friends went to the theater and purchased 3 adult tickets and one large popcorn. One adult ticket costs $9, and they spent $33.75 at the theater. Which equation could be used to determine the cost c of the popcorn? A9c - 3 = B = c C3c + 9 = D3(9) + c = 33.75

Dependent and Independent Variables Return to Table of Contents

An independent variable is one that is not influenced by another variable. The value of a dependent variable relies on the values of the independent variable. Vocabulary

Frank earns $8 per hour mowing his neighbors' lawns. The amount of money he earns m, depends on how many hours he works h. The more hours he works, the more money he earns. Therefore the dependent variable is money m, and the independent variable is hours h. The amount of hours he works does not rely on the money he earns. Example

IndependentDependent how far you drivehow much gas you use weight of childamount of dosage your test scorehow you study for the test Try to guess the missing variable. With your group, try to think of at least three examples of independent and dependent variables? IndependentDependent Click

4The number of tickets I can buy depends on how much money I have. True False A B

5So which value is the independent variable? Aamount of money Bnumber of tickets The number of tickets I can buy depends on how much money I have. Click for Question

6It costs $4.25 to rent a movie. The amount of money I spend depends on how many movies I rent. So the dependent variable is the number of movies I rent. True False A B

7The older I get, the taller I am. My height is the... AIndependent Variable BDependent Variable

8The more people I have at my party, the more brownies I need to bake. The number of people at my party is the... AIndependent Variable BDependent Variable

Equations and Tables Return to Table of Contents

The relationship between dependent and independent variables can be represented with a table. IndependentDependent InputOutput The independent variable is always in the left column, and the dependent variable is always in the right column. The relationship between independent & dependent variables and input & output works like a machine.

The value of the output relies on 1. The value of the input 2. The rule Input Output Rule The rule is the relationship between the input and the output. It says what happens to the input inside the machine. The value of the output always depends on the value of the input.

Let's Practice figuring out the rule. Step 1. Assign a value to the input. Step 2. Hit Enter to see the output. The input and output values will show on this table. Step 3. Once you have enough input/output values to figure out the rule, select + or * and the addend or factor. Step 4. Check Your Rule Click here for online practice.

n 2n click The value of n is the input. Given the value for n, find the output using the given rule. InputOutput

x + 15 $53 $70 $115 The manager of the department store raised the price $15 on each video game. $100 $38 x Price after mark up $55 Original price Can you find an expression (rule) that will satisfy the total cost of the video game if given the original price? click

g - 2 Kindergarten 8th grade 4th grade A parent wants to figure out the differences in grade level of her two sons. The younger son is two years behind the older one in terms of grade level. older son's grade level younger son's grade level g Write an expression (rule) containing a variable which satisfies the difference in grade level of the two boys. click

Tables can be used to represent equations. The table below represents the equation y = x + 3. xy The output (y) depends on the input (x). So x is the independent variable, on the left, and y is the dependent variable, on the right.

t n click This table represents the equation t = n + 11 Find the values for t, given the values for n.

Warm-up Write the equation and solve if Elizabeth has 5 crayons: Laila has three more than twice as many crayons as Elizabeth.

y x click This table represents the equation y = x - 60 Find the values for y, given the values for n.

n t This table represents the equation Find the values for t, given the values for n.

x y click This table represents the equation y = 2x Find the values for y, given the values for x.

Equations and tables can also be used to represent real-life information mathematically. Natalie is going ice skating. The skating rink charges $6.25 per hour of skating. We will let h represent the number of hours of skating and c represent the total cost. Equation: c = 6.25 h hours (h)cost (c) 1$6.25 2$ $18.75

2a Mary's age is twice the age of Jack. Jack's Age a Mary's Age Can you think of an algebraic equation which determines Mary's age (m), given Jack's age (j)? click

x + 15 $53 $70 $115 The manager of the department store raised the price $15 on each video game. $100 $38 x Price after mark up (t) $55 Original price (p) Can you find an equation that will satisfy the total cost of the video game (t) if given the original price (p)? click

9Henry downloads songs into iTunes. The amount of time it takes him to download a song depends on the song's file size. Which is the independent variable? ADownload time BFile size

10If it takes 50 seconds to download one megabyte, which equation represents this scenario ? Use the variable t for download time and s for file size. As = 50t Bt = 50s C50 - s = t

11Which table represents the equation t = 50s ? A B C D st st st st

12Find the missing value in this table. It takes Jonathan 6 minutes to run a mile. Let t represent the number of minutes and d represent the number of miles. (t)(d) 61 18?

13Use the equation y = 5x to complete the table. A B C D xy 20? ? ? ?= 4 ?= 30 ?= 250 ?= 4 ?= 30 ?= 10 ?= 100 ?= 30 ?= 250 ?= 100 ?= 3 ?= 10

Graphing Equations Return to Table of Contents

You have learned that equations and tables are two ways to represent real-life scenarios. Equations and tables can also be graphed to represent a real-life scenario. Example: A cafeteria has an automatic waffle-making machine. The table shows the relationship between the time in hours (x) and the number of waffles the machine can make (y). (x)(y)

Warm-Up If you turned in test corrections, make sure you turn in your test with the corrections. Lucy eats 3 less waffles than Bob. Write the equation to show how many waffles Lucy eats. Find the number of waffles that Lucy eats if Bob eats 1, 2, and 3 waffles.

(x) (y) The equation for this scenario is y = 50x Each hour, 50 waffles are made. This scenario can be represented with a graph. When graphing: The independent variable is always across the x axis. The dependent variable is always up the y axis. The value of y depends on the value of x. y is dependent x is independent click

Time (x) Waffles Made (y) Once you have represented the equation in a function table, you can utilize the independent and dependent variable values as coordinates. Plot the coordinates from the table below to graph the scenario.

A bookstore is running a special and is charging $5 for any childrens' book. 1. Write an equation to represent the scenario. 2. Complete the table to represent the scenario. 3. Graph the function. # of Books (x) Total Cost (y) 1

What did you do to make the equation from the chart? Find out what you do to x to get to equal y. y will always be on the side of the equation by itself and x will always have an operation happening to it to equal y. To graph points from a chart, use the values like ordered pairs and plot them on the coordinate plane. To graph points from an equation, plug in a value for x and solve to find out what y will be.

Graphing from an Equation y = 2x + 5 y = x – 5 y = 1 + x

To make an equation from points on a graph, you can put them in a chart/table of x and y values. Then find out what you do to x to get to y.

14A plane descends at a rate of 50 feet per minute. Which graph represents this scenario? A B C

15Which scenario does the graph represent? AMia earns $12 per hour. BThe river rose at a steady rate of 15 feet per hour. CThe stock value decreased by $.50 per minute DThe plane traveled 300 miles per hour.

16Which scenario does the graph represent? ATia starts out with $30. Every hour Tia earns an additional $20. BTia starts out with $50. Every minute she spends $5. CTia runs a mile every 20 minutes.

17A dogwood tree grew at the rate of 4 feet per year. Which table represents the relationship between the height of the tree (h) and the number of years (t)? A B C D th ththth th th

18The table and graph represent which equation? Ay = 50x B50y = x Cy = x - 50 Dy = x + 50 minutes (x) 1347 # of words typed (y)